Two connected pools: the free tank fills from new signups and drains two ways — conversion into the paid tank, or uninstall/inactivity. The paid tank fills from conversions and drains through monthly churn. Both pools settle into a steady state where inflow equals outflow — that equilibrium, not any single month's number, is what a subscription business is really optimizing for.
free' = acquisition − convert·free − freeChurn·free
paid' = convert·free − churn·paid
free_eq = acquisition / (convert + freeChurn)
paid_eq = convert·free_eq / churn
MRR_eq = paid_eq × price
- Raising conversion both shrinks the free-tank equilibrium and grows the paid tank — it pulls users through the funnel faster in both directions.
- Churn is the multiplier that matters most: halving churn roughly doubles the paid-tank equilibrium for the same conversion rate.
- This is the funnel/retention side of monetization — how already-acquired users flow between free and paid over time. It's a different mechanic from paid-channel acquisition, where the lever is ad spend and CAC/LTV per channel, not conversion and churn rates inside the funnel.